• Corpus ID: 166228759

# Grothendieck's Dessins d'Enfants in a Web of Dualities. II

@article{Zhou2019GrothendiecksDD,
title={Grothendieck's Dessins d'Enfants in a Web of Dualities. II},
author={Jian Zhou},
journal={arXiv: Mathematical Physics},
year={2019}
}
• Jian Zhou
• Published 26 May 2019
• Mathematics
• arXiv: Mathematical Physics
We show that the spectral curve for Eynard-Orantin topological recursions satisfied by counting Grothendieck's dessins d'enfants are related to Narayana numbers. This suggests a connection of dessins to combinatorics of Coxeter groups, noncrossing partitions, free probability theory, and cluster algebras.
12 Citations
In their recent inspiring paper Mironov and Morozov claim a surprisingly simple expansion formula for the Kontsevich-Witten tau-function in terms of the Schur Q-functions. Here we provide a similar
• Mathematics
• 2023
. Following Zhou’s framework, we consider the emergent geometry of the generalized Br´ezin-Gross-Witten models whose partition functions are known to be a family of tau-functions of the BKP
Abstract In their recent inspiring paper, Mironov and Morozov claim a surprisingly simple expansion formula for the Kontsevich-Witten tau-function in terms of the Schur Q-functions. Here we provide
• Mathematics
• 2018
We solve the problem of the computation of the orbifold Euler characteristics of $\overline{\mathcal M}_{g,n}$ using the formalism of abstract quantum field theory we develop in an earlier work.
• Mathematics
Communications in Mathematical Physics
• 2020
We prove the conjectural relationship recently proposed in Dubrovin and Yang (Commun Number Theory Phys 11:311–336, 2017) between certain special cubic Hodge integrals of the Gopakumar–Mariño–Vafa
• Mathematics
• 2022
. Given a tau-function τ ( t ) of the BKP hierarchy satisfying τ (0) = 1, we discuss how to recover its BKP-aﬃne coordinates on the isotropic Sato Grassmannian from BKP-wave function. Using this
• Mathematics
Letters in Mathematical Physics
• 2022
We derive a formula for the connected n-point functions of a tau-function of the BKP hierarchy in terms of its affine coordinates. This is a BKP-analogue of a formula for KP tau-functions proved by
• Mathematics
• 2018
A potential vector field is a solution of an extended WDVV equation which is a generalization of a WDVV equation. It is expected that potential vector fields corresponding to algebraic solutions of
• Mathematics
Annales Henri Poincaré
• 2020
We consider the Laguerre partition function and derive explicit generating functions for connected correlators with arbitrary integer powers of traces in terms of products of Hahn polynomials. It was

## References

SHOWING 1-10 OF 124 REFERENCES

We prove that the Virasoro constraints satisfied by the higher Weil–Petersson volumes of moduli spaces of curves are equivalent to Eynard–Orantin topological recursions for some spectral curve. This
• Mathematics
• 2002
We express all equivariant Gromov-Witten invariants of the projective line as matrix elements of explicit operators acting in the Fock space. As a consequence, we prove the equivariant theory is
We study the Toda conjecture of Eguchi and Yang for the Gromov-Witten invariants of CP^1,using the bihamiltonian method of the formal calculus of variations. We also study its relationship to the
In part I of this article we define the Grothendieck dessins and recall the description of the Grothendieck correspondence between dessins and Belyi pairs (X,β) where X is a compact connected Riemann
Abstract. In this paper we give necessary and sufficient conditions for a finite set of points A in $\C\cup\{\infty\}$ to be the set of cuspidal points for a Belyi function of genus zero. The most
• Mathematics
Letters in Mathematical Physics
• 2021
We consider the Dubrovin–Frobenius manifold of rank 2 whose genus expansion at a special point controls the enumeration of a higher genera generalization of the Catalan numbers, or, equivalently, the
• Mathematics
• 2002
We establish an explicit equivalence between the stationary sector of the Gromov-Witten theory of a target curve X and the enumeration of Hurwitz coverings of X in the basis of completed cycles. The
Branched covers of the complex projective line ramified over $0,1$ and $\infty$ (Grothendieck's {\em dessins d'enfant}) of fixed genus and degree are effectively enumerated. More precisely, branched
• Mathematics
• 2004
We have developed a mathematical theory of the topological vertex--a theory that was original proposed by M. Aganagic, A. Klemm, M. Marino, and C. Vafa in hep-th/0305132 on effectively computing
• Mathematics
• 2016
In 1891 Hurwitz [30] studied the number Hg,d of genus g ≥ 0 and degree d ≥ 1 coverings of the Riemann sphere with 2g + 2d− 2 fixed branch points and in particular found a closed formula for Hg,d for